Question: Vanessa is 4 years older than Kevin. Vanessa and Kevin first met 3 years ago. Eight years ago, Vanessa was 5 times older than Kevin. How old is Vanessa now?
We can use the given information to write down two equations that describe the ages of Vanessa and Kevin. Let Vanessa's current age be $v$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $v = k + 4$ Eight years ago, Vanessa was $v - 8$ years old, and Kevin was $k - 8$ years old. The information in the second sentence can be expressed in the following equation: $v - 8 = 5(k - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = v - 4$ . Substituting this into our second equation, we get the equation: $v - 8 = 5($ $(v - 4)$ $ -$ $ 8)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 8 = 5v - 60$ Solving for $v$ , we get: $4 v = 52$ $v = 13$.